Here's how the puzzle works!
Here is a list of numbers : $1,2,3,4,5,6,7,8,9$
I will give you some numbers in this list (numbers can be repeated). When receiving those numbers, you will multiply them and then find if the tens digit has a $0$. You just need to say if the new number has a $0$ in its tens digits.
Ok now, have you got a way to quickly find out if this number has a $0$ in the tens digit without just verify after multiply them ?
For example, i will give you $2,6,9$. When multiply, i get $108$. So it has a $0$ in the tens digits !
However for $2,3,3,4,4,4,5,8,8,9,9$ we get after multiplication $29 859 840$. So it hasn't a $0$ in the tens digits.
Honestly, I don't know if there is an easy way or not.
EDIT : As mentioned in the commentaries, the use of modulo makes the problem more effective. But it is still a problem when dealing with a lot of numbers. We must continue to calculate with a mod $100$ which makes the work easier. Even so, isn't there a more effective way?